You don't go through customs in the US as you are leaving. Once you arrive in MBJ you will first go through Immigration, then Baggage Claim, then Customs. No worries! (US Customs is on the way back, once you land)

You will not go thru customs from STL to ATL on your trip to Jamaica. You will go thru Jamaican Customs in Jamaica. In the states you will have to deal with TSA security which you will experience their games in STL as you begin your trip.

Plan to get to STL a few hours early to deal with the security issues that you will need to pass thru.

On your return trip if you stop at ATL then STL you will go thru customs at ATL on your return.

You won't go through customs on your way to Jamaica until you actually land at MBJ. So be happy that you only have an hour layover. The sooner you can be enjoying a red stripe! Then you will go through customs in the US on your way back home. So nothing to worry about! Enjoy!